This lecture will dwell on the memory property of capacitors.
For the RC circuit in the previous slide

vI

VI

vI

t ≥0
VI

0

t vC vC = VI + (vC (0)− VI ) e RC
−t

vC (0 )
0

t

Notice that the capacitor voltage for t ≥ 0 is independent of the form of the input voltage before t = 0 . Instead, it depends only on the capacitor voltage at t = 0 , and the input voltage for t ≥ 0 .

6.002 Fall 2000

Lecture 14

3

State
State : summary of past inputs relevant
to predicting the future

q=CV
for linear capacitors, capacitor voltage V is also state variable state variable, actually